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Numerical Simulation of Generalized Newtonian and Oldroyd-B Fluids

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • V. Prokop

    (CTU Prague)

  • K. Kozel

    (CTU Prague)

Abstract

This paper is dealing with numerical simulation of generalized Newtonian and generalized Oldroyd-B fluids. The Newtonian model of a fluid cannot capture all the phenomena in many fluids with complex microstructure, such as polymers, suspensions and granular materials. The motion of polymeric fluids is described by the conservation of mass and momentum. One shall assume that the fluid is incompressible and temperature variations are negligible. When one considers viscoelastic behavior of polymeric fluids, the extra stress tensor depends not only on the current motion of the fluid, but also on the history of the motion. In this case the extra stress tensor is decomposed into its Newtonian part and its elastic part. Components of the elastic part of the extra stress tensor are computed using the Oldroyd-B constitutive equation. Numerical solution of the arising system of equations is solved using the artificial compressibility method, finite volume method and Runge-Kutta method. Numerical methods are tested in the geometry of constricted channel.

Suggested Citation

  • V. Prokop & K. Kozel, 2013. "Numerical Simulation of Generalized Newtonian and Oldroyd-B Fluids," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 579-586, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_61
    DOI: 10.1007/978-3-642-33134-3_61
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